Finer details of last week’s intricate agreement are coming under scrutiny

WASHINGTON—The Obama administration and European Union agreed as part of the accord last week to lift sanctions over eight years on a network of Iranian scientists, military officers and companies long suspected by the U.S. and United Nations as central players in a covert nuclear weapons program.

The U.S. also agreed to remove a German engineer from its financial blacklist by late 2023 after he was targeted by sanctions for his...